EXACT-DIAGONALIZATION DEMONSTRATION OF INCOMMENSURABILITY AND THE ASSOCIATED FERMI-SURFACE FOR N-HOLES IN THE T-J MODEL

We have calculated S(q) and the single-particle distribution function [n(q)] for N holes in the t-J model on a nonsquare square-root 8 x squ are-root 32 16-site lattice with periodic boundary conditions. We just ify the use of this lattice by appealing to results obtained from the conventional 4 x 4 16-site cluster and an undoped 32-site system, each having the full square symmetry of the bulk. This new cluster has a h igh density of k points along the diagonal of reciprocal space, viz. a long k - k(1, 1). The results clearly demonstrate that when the single -hole problem has a ground state with a system momentum of k = (pi/2, pi/2), the resulting ground state for N holes involves a shift of the peak of the system's structure factor away from the antiferromagnetic state q = (pi, pi). This shift effectively increases continuously with N. When the single-hole problem has a ground state with a momentum th at is not equal to k = (pi/2, pi/2), something that may easily be acco mplished through the use of the t-t'-J model with t'/t small and posit ive, then the above-mentioned incommensurability for N holes is not fo und-the maximum of S(q) remains at q = (pi, pi) for all N. The existen ce of the incommensurate ground states are presented in conjunction wi th the electron and hole momentum distribution functions. Our results may be interpreted as evidence for rigid-band filling of the dipolar s pin distortion states of Shraiman and Siggia-by studying the hole-hole correlation function we demonstrate that the holes on our cluster ten d to stay as far apart as is possible, and thus rigid-band filling is not unexpected. Thus, these results demonstrate that in some instances important results for moderately doped CuO2 planes can be predicted f rom a knowledge of the properties of weakly doped planes. However, the electron Fermi surface that we obtain also satisfies Luttinger's theo rem, and has dimples at the wave vectors of the single-hole ground sta te, k = (+/- pi/2, +/- pi/2). Finally, we comment on the relation of a ll of these results to the incommensurability found in S(q).